Reasoning, Arithmetic, and Problem Solving
This domain tests practical math and logic used in staffing, scheduling, counts, sentence credit, and report analysis. Items are usually short word problems. The math is basic; the difficulty is reading carefully, setting up the problem, and avoiding traps such as rounding in the wrong direction.
Arithmetic you will use
Know order of operations, fractions, decimals, percentages, ratios, proportions, and averages. Staffing problems often require rounding up: if 186 inmates require one officer per 30 inmates, 186 divided by 30 is 6.2, so you need 7 officers, not 6, because a partial ratio still requires coverage. Percentage change is not the same as percentage points. A 24-hour clock converts 0130 to 1:30 a.m. and 1345 to 1:45 p.m. For sentence or release-date problems, identify the start date, the credit awarded, and whether the question asks for time served or time remaining.
Logic and reasoning
Conditional statements: "If the door is locked, the light is green" does not mean "If the light is green, the door is locked." The valid contrapositive is "If the light is not green, the door is not locked." "All A are B" does not mean "All B are A." Necessary conditions are required but may not be sufficient. On deduction items, eliminate choices that go beyond the evidence. On data items, read the table title, units, and totals before calculating.
Worked example
A unit has 240 inmates and a required ratio of one officer per 40 inmates. How many officers are needed, and how many additional officers are required if 3 are already assigned? 240 divided by 40 equals 6 officers required. 6 minus 3 equals 3 additional officers. The reasoning is to divide first, confirm the ratio is exact, and then subtract current staffing. If the result had been 5.5, you would round up to 6 because half an officer cannot cover a post.
Problem-solving steps
Read the question twice and identify what is asked. Write the units. Estimate the answer before calculating. Check whether the answer must be a whole number or a round-up. Test your result against the scenario: a release date before the arrest date, or a negative staffing number, signals an error.
Traps that cost marks
Rounding down when coverage requires rounding up; reversing the start and end times; confusing percent increase with percentage points; assuming causation from correlation; and choosing an answer that is mathematically correct but answers a different question.